A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 one year ago
1). \[\lim_{(x,y) \rightarrow (0,0)} \frac{ x ^{2}y ^{2} }{ x ^{4}+y ^{4} }\]
2). \[\lim_{(x,y) \rightarrow (0,0)} \frac{ x ^{2}y ^{2} }{ 2x ^{4}+y ^{4} }\]
In the first limit I used that \[f(x,y)=f(x,0) \rightarrow 0\] and \[f(x,y)=f(0,y)\rightarrow0\]
But in the second one that becomes totally wrong, since the xaxis goes to zero and yaxis to 1/3. Why should one change from f(o,y)> 0 to x=y in the second one, how do I recognize when I should set x=y ?
 one year ago
1). \[\lim_{(x,y) \rightarrow (0,0)} \frac{ x ^{2}y ^{2} }{ x ^{4}+y ^{4} }\] 2). \[\lim_{(x,y) \rightarrow (0,0)} \frac{ x ^{2}y ^{2} }{ 2x ^{4}+y ^{4} }\] In the first limit I used that \[f(x,y)=f(x,0) \rightarrow 0\] and \[f(x,y)=f(0,y)\rightarrow0\] But in the second one that becomes totally wrong, since the xaxis goes to zero and yaxis to 1/3. Why should one change from f(o,y)> 0 to x=y in the second one, how do I recognize when I should set x=y ?

This Question is Closed

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.0Isn't answer to 1st one 1/2 ?

experimentX
 one year ago
Best ResponseYou've already chosen the best response.0it's a double limit, you have to be a bit careful with it ... since there are multiple ways to come at (0,0), I think there is a theorem .... but currently I am busty posting my own question.

shubhamsrg
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=limit+%28x%5E2+y%5E2+%2F%28x%5E4+%2By%5E4%29%29+as+x%3E0+and+y%3E0 What does this mean ?

experimentX
 one year ago
Best ResponseYou've already chosen the best response.0says that limit does not exist, try y=x or y=x^2, if you don't get the same limit then limit does not exist.

frx
 one year ago
Best ResponseYou've already chosen the best response.0According to the answerkey to Adams Calculus the answer for the first one is 0 and the second one DNE

Zarkon
 one year ago
Best ResponseYou've already chosen the best response.0\[\lim_{(x,y) \rightarrow (0,0)} \frac{ x ^{2}y ^{2} }{ x ^{4}+y ^{4} }\] let \(y=mx\) then \[\lim_{x \rightarrow 0} \frac{ x ^{2}(mx) ^{2} }{ x ^{4}+(mx) ^{4} }\] \[\lim_{x \rightarrow 0} \frac{ m^2x ^{4} }{ x ^{4}(1+m ^{4}) }\] \[\lim_{x \rightarrow 0} \frac{ m^2 }{ 1+m ^{4} }=\frac{ m^2 }{ 1+m ^{4} }\] pick any real number \(m\)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.